# Properties

 Label 446400.lx Number of curves $6$ Conductor $446400$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("446400.lx1")

sage: E.isogeny_class()

## Elliptic curves in class 446400.lx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
446400.lx1 446400lx6 [0, 0, 0, -4428288300, -113423212798000] [2] 150994944
446400.lx2 446400lx4 [0, 0, 0, -276768300, -1772233918000] [2, 2] 75497472
446400.lx3 446400lx5 [0, 0, 0, -272448300, -1830234238000] [2] 150994944
446400.lx4 446400lx3 [0, 0, 0, -53280300, 116709698000] [2] 75497472 $$\Gamma_0(N)$$-optimal*
446400.lx5 446400lx2 [0, 0, 0, -17568300, -26781118000] [2, 2] 37748736 $$\Gamma_0(N)$$-optimal*
446400.lx6 446400lx1 [0, 0, 0, 863700, -1750462000] [2] 18874368 $$\Gamma_0(N)$$-optimal*
*optimality has not been proved rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 446400.lx6.

## Rank

sage: E.rank()

The elliptic curves in class 446400.lx have rank $$0$$.

## Modular form 446400.2.a.lx

sage: E.q_eigenform(10)

$$q + 4q^{11} + 6q^{13} + 2q^{17} + 4q^{19} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.